From closed to open one-dimensional Anderson model: transport versus spectral statistics

Using the phenomenological expression for the level spacing distribution with only one parameter 0 ≤ β ≤ ∞ covering all regimes of chaos and complexity in a quantum system, we show that transport properties of the one-dimensional Anderson model of finite size can be expressed in terms of this parameter. Specifically, we demonstrate a strictly linear relation between β and the normalized localization length for the whole transition from strongly localized to extended states. This result allows one to describe all transport properties in the open system entirely in terms of the parameter β and the strength of the coupling to the continuum. For nonperfect coupling, our data show a quite unusual interplay between the degree of internal chaos defined by β and the degree of openness of the model. The results can be experimentally tested in single-mode waveguides with either bulk or surface disorder.